LMFDB - Embedded newform 85.2.e.a.81.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(21,85)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("85.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.5
Root			$0.455023i$ of defining polynomial
Character	$\chi$	$=$	85.81
Dual form			85.2.e.a.21.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.783476i q^{2} +(0.385357 + 0.385357i) q^{3} +1.38617 q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.301918 + 0.301918i) q^{6} +(-0.840380 + 0.840380i) q^{7} +2.65298i q^{8} -2.70300i q^{9} +(0.554001 - 0.554001i) q^{10} +(-1.80608 + 1.80608i) q^{11} +(0.534168 + 0.534168i) q^{12} -0.368117 q^{13} +(-0.658417 - 0.658417i) q^{14} -0.544977i q^{15} +0.693788 q^{16} +(-2.46531 - 3.30488i) q^{17} +2.11773 q^{18} -6.61138i q^{19} +(-0.980167 - 0.980167i) q^{20} -0.647692 q^{21} +(-1.41502 - 1.41502i) q^{22} +(-2.73186 + 2.73186i) q^{23} +(-1.02234 + 1.02234i) q^{24} +1.00000i q^{25} -0.288411i q^{26} +(2.19769 - 2.19769i) q^{27} +(-1.16491 + 1.16491i) q^{28} +(-1.63466 - 1.63466i) q^{29} +0.426976 q^{30} +(4.68480 + 4.68480i) q^{31} +5.84952i q^{32} -1.39197 q^{33} +(2.58929 - 1.93151i) q^{34} +1.18848 q^{35} -3.74681i q^{36} +(2.24619 + 2.24619i) q^{37} +5.17986 q^{38} +(-0.141856 - 0.141856i) q^{39} +(1.87594 - 1.87594i) q^{40} +(-5.16572 + 5.16572i) q^{41} -0.507451i q^{42} +6.82350i q^{43} +(-2.50353 + 2.50353i) q^{44} +(-1.91131 + 1.91131i) q^{45} +(-2.14034 - 2.14034i) q^{46} +7.80793 q^{47} +(0.267356 + 0.267356i) q^{48} +5.58752i q^{49} -0.783476 q^{50} +(0.323534 - 2.22358i) q^{51} -0.510272 q^{52} -8.01219i q^{53} +(1.72184 + 1.72184i) q^{54} +2.55419 q^{55} +(-2.22951 - 2.22951i) q^{56} +(2.54774 - 2.54774i) q^{57} +(1.28072 - 1.28072i) q^{58} +5.22381i q^{59} -0.755428i q^{60} +(5.74267 - 5.74267i) q^{61} +(-3.67043 + 3.67043i) q^{62} +(2.27155 + 2.27155i) q^{63} -3.19538 q^{64} +(0.260298 + 0.260298i) q^{65} -1.09058i q^{66} -7.94564 q^{67} +(-3.41733 - 4.58111i) q^{68} -2.10548 q^{69} +0.931143i q^{70} +(8.40610 + 8.40610i) q^{71} +7.17100 q^{72} +(-10.4176 - 10.4176i) q^{73} +(-1.75984 + 1.75984i) q^{74} +(-0.385357 + 0.385357i) q^{75} -9.16447i q^{76} -3.03559i q^{77} +(0.111141 - 0.111141i) q^{78} +(0.575011 - 0.575011i) q^{79} +(-0.490582 - 0.490582i) q^{80} -6.41521 q^{81} +(-4.04721 - 4.04721i) q^{82} -3.99116i q^{83} -0.897809 q^{84} +(-0.593666 + 4.08014i) q^{85} -5.34604 q^{86} -1.25986i q^{87} +(-4.79150 - 4.79150i) q^{88} +9.14311 q^{89} +(-1.49746 - 1.49746i) q^{90} +(0.309359 - 0.309359i) q^{91} +(-3.78681 + 3.78681i) q^{92} +3.61064i q^{93} +6.11732i q^{94} +(-4.67495 + 4.67495i) q^{95} +(-2.25415 + 2.25415i) q^{96} +(-4.99529 - 4.99529i) q^{97} -4.37769 q^{98} +(4.88185 + 4.88185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.783476i			0.554001i	0.960870	+	0.277000i	$0.0893404\pi$
$2$			0.783476i			0.554001i	−0.960870	+	0.277000i	$0.910660\pi$
$3$	0.385357	+	0.385357i	0.222486	+	0.222486i	0.809544	−	0.587059i	$-0.199714\pi$
$3$	0.385357	+	0.385357i	0.222486	+	0.222486i	−0.587059	+	0.809544i	$0.699714\pi$
$4$	1.38617			0.693083
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−0.301918	+	0.301918i	−0.123257	+	0.123257i
$7$	−0.840380	+	0.840380i	−0.317634	+	0.317634i	−0.847858	−	0.530224i	$-0.822108\pi$
$7$	−0.840380	+	0.840380i	−0.317634	+	0.317634i	0.530224	+	0.847858i	$0.322108\pi$
$8$			2.65298i			0.937970i
$9$		−	2.70300i		−	0.901000i
$10$	0.554001	−	0.554001i	0.175190	−	0.175190i
$11$	−1.80608	+	1.80608i	−0.544555	+	0.544555i	−0.924861	−	0.380306i	$-0.875819\pi$
$11$	−1.80608	+	1.80608i	−0.544555	+	0.544555i	0.380306	+	0.924861i	$0.375819\pi$
$12$	0.534168	+	0.534168i	0.154201	+	0.154201i
$13$	−0.368117			−0.102097			−0.0510487	−	0.998696i	$-0.516256\pi$
$13$	−0.368117			−0.102097			−0.0510487	+	0.998696i	$0.516256\pi$
$14$	−0.658417	−	0.658417i	−0.175969	−	0.175969i
$15$		−	0.544977i		−	0.140712i
$16$	0.693788			0.173447
$17$	−2.46531	−	3.30488i	−0.597926	−	0.801552i
$17$	−2.46531	−	3.30488i	−0.597926	−	0.801552i
$18$	2.11773			0.499155
$19$		−	6.61138i		−	1.51676i	−0.651816	−	0.758378i	$-0.725992\pi$
$19$		−	6.61138i		−	1.51676i	0.651816	−	0.758378i	$-0.274008\pi$
$20$	−0.980167	−	0.980167i	−0.219172	−	0.219172i
$21$	−0.647692			−0.141338
$22$	−1.41502	−	1.41502i	−0.301684	−	0.301684i
$23$	−2.73186	+	2.73186i	−0.569632	+	0.569632i	−0.932025	−	0.362394i	$-0.881960\pi$
$23$	−2.73186	+	2.73186i	−0.569632	+	0.569632i	0.362394	+	0.932025i	$0.381960\pi$
$24$	−1.02234	+	1.02234i	−0.208685	+	0.208685i
$25$			1.00000i			0.200000i
$26$		−	0.288411i		−	0.0565621i
$27$	2.19769	−	2.19769i	0.422945	−	0.422945i
$28$	−1.16491	+	1.16491i	−0.220147	+	0.220147i
$29$	−1.63466	−	1.63466i	−0.303549	−	0.303549i	0.538851	−	0.842401i	$-0.318858\pi$
$29$	−1.63466	−	1.63466i	−0.303549	−	0.303549i	−0.842401	+	0.538851i	$0.818858\pi$
$30$	0.426976			0.0779548
$31$	4.68480	+	4.68480i	0.841415	+	0.841415i	0.989043	−	0.147628i	$-0.0471639\pi$
$31$	4.68480	+	4.68480i	0.841415	+	0.841415i	−0.147628	+	0.989043i	$0.547164\pi$
$32$			5.84952i			1.03406i
$33$	−1.39197			−0.242311
$34$	2.58929	−	1.93151i	0.444060	−	0.331251i
$35$	1.18848			0.200889
$36$		−	3.74681i		−	0.624468i
$37$	2.24619	+	2.24619i	0.369271	+	0.369271i	0.867211	−	0.497940i	$-0.165910\pi$
$37$	2.24619	+	2.24619i	0.369271	+	0.369271i	−0.497940	+	0.867211i	$0.665910\pi$
$38$	5.17986			0.840284
$39$	−0.141856	−	0.141856i	−0.0227152	−	0.0227152i
$40$	1.87594	−	1.87594i	0.296612	−	0.296612i
$41$	−5.16572	+	5.16572i	−0.806749	+	0.806749i	−0.984140	−	0.177391i	$-0.943234\pi$
$41$	−5.16572	+	5.16572i	−0.806749	+	0.806749i	0.177391	+	0.984140i	$0.443234\pi$
$42$		−	0.507451i		−	0.0783014i
$43$			6.82350i			1.04057i	0.853992	+	0.520287i	$0.174175\pi$
$43$			6.82350i			1.04057i	−0.853992	+	0.520287i	$0.825825\pi$
$44$	−2.50353	+	2.50353i	−0.377422	+	0.377422i
$45$	−1.91131	+	1.91131i	−0.284921	+	0.284921i
$46$	−2.14034	−	2.14034i	−0.315576	−	0.315576i
$47$	7.80793			1.13890			0.569452	−	0.822025i	$-0.307156\pi$
$47$	7.80793			1.13890			0.569452	+	0.822025i	$0.307156\pi$
$48$	0.267356	+	0.267356i	0.0385895	+	0.0385895i
$49$			5.58752i			0.798218i
$50$	−0.783476			−0.110800
$51$	0.323534	−	2.22358i	0.0453038	−	0.311364i
$52$	−0.510272			−0.0707620
$53$		−	8.01219i		−	1.10056i	−0.834980	−	0.550280i	$-0.814521\pi$
$53$		−	8.01219i		−	1.10056i	0.834980	−	0.550280i	$-0.185479\pi$
$54$	1.72184	+	1.72184i	0.234312	+	0.234312i
$55$	2.55419			0.344407
$56$	−2.22951	−	2.22951i	−0.297931	−	0.297931i
$57$	2.54774	−	2.54774i	0.337456	−	0.337456i
$58$	1.28072	−	1.28072i	0.168167	−	0.168167i
$59$			5.22381i			0.680082i	0.940411	+	0.340041i	$0.110441\pi$
$59$			5.22381i			0.680082i	−0.940411	+	0.340041i	$0.889559\pi$
$60$		−	0.755428i		−	0.0975253i
$61$	5.74267	−	5.74267i	0.735273	−	0.735273i	−0.236386	−	0.971659i	$-0.575963\pi$
$61$	5.74267	−	5.74267i	0.735273	−	0.735273i	0.971659	+	0.236386i	$0.0759630\pi$
$62$	−3.67043	+	3.67043i	−0.466145	+	0.466145i
$63$	2.27155	+	2.27155i	0.286188	+	0.286188i
$64$	−3.19538			−0.399423
$65$	0.260298	+	0.260298i	0.0322860	+	0.0322860i
$66$		−	1.09058i		−	0.134241i
$67$	−7.94564			−0.970715			−0.485357	−	0.874316i	$-0.661310\pi$
$67$	−7.94564			−0.970715			−0.485357	+	0.874316i	$0.661310\pi$
$68$	−3.41733	−	4.58111i	−0.414412	−	0.555542i
$69$	−2.10548			−0.253470
$70$			0.931143i			0.111293i
$71$	8.40610	+	8.40610i	0.997621	+	0.997621i	0.999997	−	0.00237624i	$-0.000756380\pi$
$71$	8.40610	+	8.40610i	0.997621	+	0.997621i	−0.00237624	+	0.999997i	$0.500756\pi$
$72$	7.17100			0.845111
$73$	−10.4176	−	10.4176i	−1.21929	−	1.21929i	−0.967881	−	0.251409i	$-0.919106\pi$
$73$	−10.4176	−	10.4176i	−1.21929	−	1.21929i	−0.251409	−	0.967881i	$-0.580894\pi$
$74$	−1.75984	+	1.75984i	−0.204577	+	0.204577i
$75$	−0.385357	+	0.385357i	−0.0444972	+	0.0444972i
$76$		−	9.16447i		−	1.05124i
$77$		−	3.03559i		−	0.345938i
$78$	0.111141	−	0.111141i	0.0125843	−	0.0125843i
$79$	0.575011	−	0.575011i	0.0646938	−	0.0646938i	−0.674020	−	0.738713i	$-0.735434\pi$
$79$	0.575011	−	0.575011i	0.0646938	−	0.0646938i	0.738713	+	0.674020i	$0.235434\pi$
$80$	−0.490582	−	0.490582i	−0.0548488	−	0.0548488i
$81$	−6.41521			−0.712801
$82$	−4.04721	−	4.04721i	−0.446940	−	0.446940i
$83$		−	3.99116i		−	0.438087i	−0.975715	−	0.219044i	$-0.929706\pi$
$83$		−	3.99116i		−	0.438087i	0.975715	−	0.219044i	$-0.0702937\pi$
$84$	−0.897809			−0.0979590
$85$	−0.593666	+	4.08014i	−0.0643921	+	0.442554i
$86$	−5.34604			−0.576479
$87$		−	1.25986i		−	0.135071i
$88$	−4.79150	−	4.79150i	−0.510776	−	0.510776i
$89$	9.14311			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$89$	9.14311			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$90$	−1.49746	−	1.49746i	−0.157847	−	0.157847i
$91$	0.309359	−	0.309359i	0.0324296	−	0.0324296i
$92$	−3.78681	+	3.78681i	−0.394802	+	0.394802i
$93$			3.61064i			0.374406i
$94$			6.11732i			0.630953i
$95$	−4.67495	+	4.67495i	−0.479640	+	0.479640i
$96$	−2.25415	+	2.25415i	−0.230063	+	0.230063i
$97$	−4.99529	−	4.99529i	−0.507195	−	0.507195i	0.406470	−	0.913664i	$-0.366760\pi$
$97$	−4.99529	−	4.99529i	−0.507195	−	0.507195i	−0.913664	+	0.406470i	$0.866760\pi$
$98$	−4.37769			−0.442213
$99$	4.88185	+	4.88185i	0.490644	+	0.490644i
$100$			1.38617i			0.138617i
$101$	0.296263			0.0294793			0.0147396	−	0.999891i	$-0.495308\pi$
$101$	0.296263			0.0294793			0.0147396	+	0.999891i	$0.495308\pi$
$102$	1.74212	+	0.253481i	0.172496	+	0.0250984i
$103$	17.0372			1.67873			0.839363	−	0.543571i	$-0.182928\pi$
$103$	17.0372			1.67873			0.839363	+	0.543571i	$0.182928\pi$
$104$		−	0.976608i		−	0.0957642i
$105$	0.457987	+	0.457987i	0.0446950	+	0.0446950i
$106$	6.27736			0.609711
$107$	−2.69319	−	2.69319i	−0.260360	−	0.260360i	0.564840	−	0.825200i	$-0.308938\pi$
$107$	−2.69319	−	2.69319i	−0.260360	−	0.260360i	−0.825200	+	0.564840i	$0.808938\pi$
$108$	3.04636	−	3.04636i	0.293136	−	0.293136i
$109$	−8.51171	+	8.51171i	−0.815274	+	0.815274i	−0.985419	−	0.170145i	$-0.945576\pi$
$109$	−8.51171	+	8.51171i	−0.815274	+	0.815274i	0.170145	+	0.985419i	$0.445576\pi$
$110$			2.00114i			0.190802i
$111$			1.73117i			0.164315i
$112$	−0.583046	+	0.583046i	−0.0550926	+	0.0550926i
$113$	11.6545	−	11.6545i	1.09636	−	1.09636i	0.101526	−	0.994833i	$-0.467628\pi$
$113$	11.6545	−	11.6545i	1.09636	−	1.09636i	0.994833	−	0.101526i	$-0.0323724\pi$
$114$	1.99609	+	1.99609i	0.186951	+	0.186951i
$115$	3.86343			0.360267
$116$	−2.26592	−	2.26592i	−0.210385	−	0.210385i
$117$			0.995022i			0.0919898i
$118$	−4.09272			−0.376766
$119$	4.84915	+	0.705558i	0.444521	+	0.0646784i
$120$	1.44581			0.131984
$121$			4.47612i			0.406920i
$122$	4.49924	+	4.49924i	0.407342	+	0.407342i
$123$	−3.98129			−0.358980
$124$	6.49391	+	6.49391i	0.583170	+	0.583170i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−1.77970	+	1.77970i	−0.158548	+	0.158548i
$127$		−	4.48798i		−	0.398244i	−0.979975	−	0.199122i	$-0.936191\pi$
$127$		−	4.48798i		−	0.398244i	0.979975	−	0.199122i	$-0.0638090\pi$
$128$			9.19554i			0.812779i
$129$	−2.62948	+	2.62948i	−0.231513	+	0.231513i
$130$	−0.203937	+	0.203937i	−0.0178865	+	0.0178865i
$131$	−6.60646	−	6.60646i	−0.577209	−	0.577209i	0.356924	−	0.934133i	$-0.383826\pi$
$131$	−6.60646	−	6.60646i	−0.577209	−	0.577209i	−0.934133	+	0.356924i	$0.883826\pi$
$132$	−1.92951			−0.167942
$133$	5.55607	+	5.55607i	0.481773	+	0.481773i
$134$		−	6.22522i		−	0.537777i
$135$	−3.10800			−0.267494
$136$	8.76778	−	6.54042i	0.751831	−	0.560836i
$137$	8.47822			0.724344			0.362172	−	0.932111i	$-0.382035\pi$
$137$	8.47822			0.724344			0.362172	+	0.932111i	$0.382035\pi$
$138$		−	1.64959i		−	0.140423i
$139$	−4.24761	−	4.24761i	−0.360277	−	0.360277i	0.503638	−	0.863915i	$-0.331995\pi$
$139$	−4.24761	−	4.24761i	−0.360277	−	0.360277i	−0.863915	+	0.503638i	$0.831995\pi$
$140$	1.64743			0.139233
$141$	3.00884	+	3.00884i	0.253390	+	0.253390i
$142$	−6.58598	+	6.58598i	−0.552683	+	0.552683i
$143$	0.664851	−	0.664851i	0.0555976	−	0.0555976i
$144$		−	1.87531i		−	0.156276i
$145$			2.31176i			0.191982i
$146$	8.16195	−	8.16195i	0.675488	−	0.675488i
$147$	−2.15319	+	2.15319i	−0.177592	+	0.177592i
$148$	3.11359	+	3.11359i	0.255936	+	0.255936i
$149$	9.11821			0.746993			0.373497	−	0.927632i	$-0.378159\pi$
$149$	9.11821			0.746993			0.373497	+	0.927632i	$0.378159\pi$
$150$	−0.301918	−	0.301918i	−0.0246515	−	0.0246515i
$151$			13.1144i			1.06724i	0.845725	+	0.533619i	$0.179168\pi$
$151$			13.1144i			1.06724i	−0.845725	+	0.533619i	$0.820832\pi$
$152$	17.5399			1.42267
$153$	−8.93310	+	6.66374i	−0.722198	+	0.538731i
$154$	2.37831			0.191650
$155$		−	6.62531i		−	0.532157i
$156$	−0.196637	−	0.196637i	−0.0157435	−	0.0157435i
$157$	−20.0496			−1.60013			−0.800065	−	0.599913i	$-0.795202\pi$
$157$	−20.0496			−1.60013			−0.800065	+	0.599913i	$0.795202\pi$
$158$	0.450507	+	0.450507i	0.0358404	+	0.0358404i
$159$	3.08755	−	3.08755i	0.244859	−	0.244859i
$160$	4.13624	−	4.13624i	0.326998	−	0.326998i
$161$		−	4.59160i		−	0.361869i
$162$		−	5.02616i		−	0.394893i
$163$	−10.0910	+	10.0910i	−0.790386	+	0.790386i	−0.981557	−	0.191170i	$-0.938772\pi$
$163$	−10.0910	+	10.0910i	−0.790386	+	0.790386i	0.191170	+	0.981557i	$0.438772\pi$
$164$	−7.16054	+	7.16054i	−0.559144	+	0.559144i
$165$	0.984274	+	0.984274i	0.0766256	+	0.0766256i
$166$	3.12698			0.242701
$167$	−0.157215	−	0.157215i	−0.0121656	−	0.0121656i	0.700998	−	0.713163i	$-0.252738\pi$
$167$	−0.157215	−	0.157215i	−0.0121656	−	0.0121656i	−0.713163	+	0.700998i	$0.752738\pi$
$168$		−	1.71831i		−	0.132571i
$169$	−12.8645			−0.989576
$170$	−3.19669	−	0.465123i	−0.245175	−	0.0356733i
$171$	−17.8706			−1.36660
$172$			9.45850i			0.721204i
$173$	−14.1383	−	14.1383i	−1.07492	−	1.07492i	−0.996957	−	0.0779592i	$-0.975160\pi$
$173$	−14.1383	−	14.1383i	−1.07492	−	1.07492i	−0.0779592	−	0.996957i	$-0.524840\pi$
$174$	0.987067			0.0748294
$175$	−0.840380	−	0.840380i	−0.0635268	−	0.0635268i
$176$	−1.25304	+	1.25304i	−0.0944514	+	0.0944514i
$177$	−2.01303	+	2.01303i	−0.151308	+	0.151308i
$178$			7.16341i			0.536920i
$179$		−	24.3120i		−	1.81716i	−0.417708	−	0.908581i	$-0.637166\pi$
$179$		−	24.3120i		−	1.81716i	0.417708	−	0.908581i	$-0.362834\pi$
$180$	−2.64939	+	2.64939i	−0.197474	+	0.197474i
$181$	8.40507	−	8.40507i	0.624744	−	0.624744i	−0.321997	−	0.946741i	$-0.604354\pi$
$181$	8.40507	−	8.40507i	0.624744	−	0.624744i	0.946741	+	0.321997i	$0.104354\pi$
$182$	0.242375	+	0.242375i	0.0179660	+	0.0179660i
$183$	4.42595			0.327176
$184$	−7.24756	−	7.24756i	−0.534297	−	0.534297i
$185$		−	3.17659i		−	0.233548i
$186$	−2.82885			−0.207421
$187$	10.4215	+	1.51634i	0.762092	+	0.110885i
$188$	10.8231			0.789354
$189$			3.69379i			0.268684i
$190$	−3.66271	−	3.66271i	−0.265721	−	0.265721i
$191$	−17.2930			−1.25128			−0.625638	−	0.780114i	$-0.715161\pi$
$191$	−17.2930			−1.25128			−0.625638	+	0.780114i	$0.715161\pi$
$192$	−1.23136	−	1.23136i	−0.0888659	−	0.0888659i
$193$	1.27952	−	1.27952i	0.0921022	−	0.0921022i	−0.659555	−	0.751657i	$-0.729255\pi$
$193$	1.27952	−	1.27952i	0.0921022	−	0.0921022i	0.751657	+	0.659555i	$0.229255\pi$
$194$	3.91369	−	3.91369i	0.280986	−	0.280986i
$195$			0.200615i			0.0143664i
$196$			7.74523i			0.553231i
$197$	11.7227	−	11.7227i	0.835207	−	0.835207i	−0.153017	−	0.988224i	$-0.548899\pi$
$197$	11.7227	−	11.7227i	0.835207	−	0.835207i	0.988224	+	0.153017i	$0.0488989\pi$
$198$	−3.82481	+	3.82481i	−0.271817	+	0.271817i
$199$	−17.7915	−	17.7915i	−1.26121	−	1.26121i	−0.950509	−	0.310698i	$-0.899437\pi$
$199$	−17.7915	−	17.7915i	−1.26121	−	1.26121i	−0.310698	−	0.950509i	$-0.600563\pi$
$200$	−2.65298			−0.187594
$201$	−3.06191	−	3.06191i	−0.215970	−	0.215970i
$202$			0.232115i			0.0163315i
$203$	2.74748			0.192835
$204$	0.448472	−	3.08225i	0.0313993	−	0.215801i
$205$	7.30543			0.510233
$206$			13.3482i			0.930016i
$207$	7.38421	+	7.38421i	0.513238	+	0.513238i
$208$	−0.255396			−0.0177085
$209$	11.9407	+	11.9407i	0.825956	+	0.825956i
$210$	−0.358822	+	0.358822i	−0.0247611	+	0.0247611i
$211$	5.94554	−	5.94554i	0.409308	−	0.409308i	−0.472189	−	0.881497i	$-0.656536\pi$
$211$	5.94554	−	5.94554i	0.409308	−	0.409308i	0.881497	+	0.472189i	$0.156536\pi$
$212$		−	11.1062i		−	0.762779i
$213$			6.47870i			0.443913i
$214$	2.11005	−	2.11005i	0.144240	−	0.144240i
$215$	4.82494	−	4.82494i	0.329058	−	0.329058i
$216$	5.83042	+	5.83042i	0.396710	+	0.396710i
$217$	−7.87402			−0.534524
$218$	−6.66872	−	6.66872i	−0.451663	−	0.451663i
$219$		−	8.02900i		−	0.542549i
$220$	3.54053			0.238702
$221$	0.907524	+	1.21658i	0.0610467	+	0.0818363i
$222$	−1.35633			−0.0910308
$223$			16.5499i			1.10826i	0.832429	+	0.554132i	$0.186950\pi$
$223$			16.5499i			1.10826i	−0.832429	+	0.554132i	$0.813050\pi$
$224$	−4.91582	−	4.91582i	−0.328452	−	0.328452i
$225$	2.70300			0.180200
$226$	9.13098	+	9.13098i	0.607384	+	0.607384i
$227$	−5.03248	+	5.03248i	−0.334017	+	0.334017i	−0.854110	−	0.520093i	$-0.825897\pi$
$227$	−5.03248	+	5.03248i	−0.334017	+	0.334017i	0.520093	+	0.854110i	$0.325897\pi$
$228$	3.53159	−	3.53159i	0.233885	−	0.233885i
$229$		−	1.46774i		−	0.0969907i	−0.998823	−	0.0484953i	$-0.984557\pi$
$229$		−	1.46774i		−	0.0969907i	0.998823	−	0.0484953i	$-0.0154426\pi$
$230$			3.02690i			0.199588i
$231$	1.16979	−	1.16979i	0.0769663	−	0.0769663i
$232$	4.33673	−	4.33673i	0.284720	−	0.284720i
$233$	16.3810	+	16.3810i	1.07316	+	1.07316i	0.997104	+	0.0760541i	$0.0242322\pi$
$233$	16.3810	+	16.3810i	1.07316	+	1.07316i	0.0760541	+	0.997104i	$0.475768\pi$
$234$	−0.779575			−0.0509624
$235$	−5.52104	−	5.52104i	−0.360153	−	0.360153i
$236$			7.24106i			0.471353i
$237$	0.443169			0.0287869
$238$	−0.552788	+	3.79919i	−0.0358319	+	0.246265i
$239$	−6.43252			−0.416085			−0.208042	−	0.978120i	$-0.566709\pi$
$239$	−6.43252			−0.416085			−0.208042	+	0.978120i	$0.566709\pi$
$240$		−	0.378098i		−	0.0244061i
$241$	19.3719	+	19.3719i	1.24785	+	1.24785i	0.956667	+	0.291183i	$0.0940490\pi$
$241$	19.3719	+	19.3719i	1.24785	+	1.24785i	0.291183	+	0.956667i	$0.405951\pi$
$242$	−3.50693			−0.225434
$243$	−9.06521	−	9.06521i	−0.581534	−	0.581534i
$244$	7.96029	−	7.96029i	0.509605	−	0.509605i
$245$	3.95098	−	3.95098i	0.252419	−	0.252419i
$246$		−	3.11924i		−	0.198875i
$247$			2.43376i			0.154857i
$248$	−12.4287	+	12.4287i	−0.789221	+	0.789221i
$249$	1.53802	−	1.53802i	0.0974681	−	0.0974681i
$250$	0.554001	+	0.554001i	0.0350381	+	0.0350381i
$251$	0.234413			0.0147960			0.00739800	−	0.999973i	$-0.497645\pi$
$251$	0.234413			0.0147960			0.00739800	+	0.999973i	$0.497645\pi$
$252$	3.14874	+	3.14874i	0.198352	+	0.198352i
$253$		−	9.86793i		−	0.620391i
$254$	3.51623			0.220628
$255$	−1.80108	+	1.34354i	−0.112788	+	0.0841355i
$256$	−13.5952			−0.849703
$257$			3.56040i			0.222092i	0.993815	+	0.111046i	$0.0354201\pi$
$257$			3.56040i			0.222092i	−0.993815	+	0.111046i	$0.964580\pi$
$258$	−2.06013	−	2.06013i	−0.128258	−	0.128258i
$259$	−3.77531			−0.234586
$260$	0.360817	+	0.360817i	0.0223769	+	0.0223769i
$261$	−4.41850	+	4.41850i	−0.273498	+	0.273498i
$262$	5.17600	−	5.17600i	0.319775	−	0.319775i
$263$			30.0000i			1.84988i	0.380112	+	0.924940i	$0.375885\pi$
$263$			30.0000i			1.84988i	−0.380112	+	0.924940i	$0.624115\pi$
$264$		−	3.69287i		−	0.227281i
$265$	−5.66547	+	5.66547i	−0.348027	+	0.348027i
$266$	−4.35305	+	4.35305i	−0.266902	+	0.266902i
$267$	3.52336	+	3.52336i	0.215626	+	0.215626i
$268$	−11.0140			−0.672786
$269$	−0.268165	−	0.268165i	−0.0163503	−	0.0163503i	0.698884	−	0.715235i	$-0.253680\pi$
$269$	−0.268165	−	0.268165i	−0.0163503	−	0.0163503i	−0.715235	+	0.698884i	$0.753680\pi$
$270$		−	2.43504i		−	0.148192i
$271$	10.6144			0.644780			0.322390	−	0.946607i	$-0.395514\pi$
$271$	10.6144			0.644780			0.322390	+	0.946607i	$0.395514\pi$
$272$	−1.71040	−	2.29289i	−0.103708	−	0.139027i
$273$	0.238427			0.0144302
$274$			6.64248i			0.401287i
$275$	−1.80608	−	1.80608i	−0.108911	−	0.108911i
$276$	−2.91854			−0.175676
$277$	21.5614	+	21.5614i	1.29550	+	1.29550i	0.931334	+	0.364167i	$0.118646\pi$
$277$	21.5614	+	21.5614i	1.29550	+	1.29550i	0.364167	+	0.931334i	$0.381354\pi$
$278$	3.32790	−	3.32790i	0.199594	−	0.199594i
$279$	12.6630	−	12.6630i	0.758115	−	0.758115i
$280$			3.15300i			0.188428i
$281$		−	26.4402i		−	1.57729i	−0.614849	−	0.788645i	$-0.710783\pi$
$281$		−	26.4402i		−	1.57729i	0.614849	−	0.788645i	$-0.289217\pi$
$282$	−2.35735	+	2.35735i	−0.140378	+	0.140378i
$283$	13.1353	−	13.1353i	0.780813	−	0.780813i	−0.199155	−	0.979968i	$-0.563820\pi$
$283$	13.1353	−	13.1353i	0.780813	−	0.780813i	0.979968	+	0.199155i	$0.0638198\pi$
$284$	11.6523	+	11.6523i	0.691434	+	0.691434i
$285$	−3.60305			−0.213426
$286$	0.520895	+	0.520895i	0.0308011	+	0.0308011i
$287$		−	8.68233i		−	0.512502i
$288$	15.8113			0.931688
$289$	−4.84448	+	16.2951i	−0.284970	+	0.958537i
$290$	−1.81121			−0.106358
$291$		−	3.84993i		−	0.225687i
$292$	−14.4405	−	14.4405i	−0.845069	−	0.845069i
$293$	3.59958			0.210289			0.105145	−	0.994457i	$-0.466469\pi$
$293$	3.59958			0.210289			0.105145	+	0.994457i	$0.466469\pi$
$294$	−1.68697	−	1.68697i	−0.0983861	−	0.0983861i
$295$	3.69379	−	3.69379i	0.215061	−	0.215061i
$296$	−5.95910	+	5.95910i	−0.346365	+	0.346365i
$297$			7.93842i			0.460634i
$298$			7.14390i			0.413835i
$299$	1.00564	−	1.00564i	0.0581579	−	0.0581579i
$300$	−0.534168	+	0.534168i	−0.0308402	+	0.0308402i
$301$	−5.73433	−	5.73433i	−0.330521	−	0.330521i
$302$	−10.2748			−0.591251
$303$	0.114167	+	0.114167i	0.00655872	+	0.00655872i
$304$		−	4.58690i		−	0.263077i
$305$	−8.12136			−0.465027
$306$	−5.22087	−	6.99886i	−0.298458	−	0.400098i
$307$	−33.4128			−1.90697			−0.953486	−	0.301438i	$-0.902533\pi$
$307$	−33.4128			−1.90697			−0.953486	+	0.301438i	$0.902533\pi$
$308$		−	4.20784i		−	0.239764i
$309$	6.56540	+	6.56540i	0.373493	+	0.373493i
$310$	5.19077			0.294816
$311$	9.75529	+	9.75529i	0.553172	+	0.553172i	0.927355	−	0.374183i	$-0.122077\pi$
$311$	9.75529	+	9.75529i	0.553172	+	0.553172i	−0.374183	+	0.927355i	$0.622077\pi$
$312$	0.376342	−	0.376342i	0.0213062	−	0.0213062i
$313$	21.6164	−	21.6164i	1.22183	−	1.22183i	0.254853	−	0.966980i	$-0.417973\pi$
$313$	21.6164	−	21.6164i	1.22183	−	1.22183i	0.966980	−	0.254853i	$-0.0820271\pi$
$314$		−	15.7084i		−	0.886473i
$315$		−	3.21245i		−	0.181001i
$316$	0.797061	−	0.797061i	0.0448382	−	0.0448382i
$317$	−2.27476	+	2.27476i	−0.127763	+	0.127763i	−0.768097	−	0.640334i	$-0.778796\pi$
$317$	−2.27476	+	2.27476i	−0.127763	+	0.127763i	0.640334	+	0.768097i	$0.278796\pi$
$318$	2.41902	+	2.41902i	0.135652	+	0.135652i
$319$	5.90468			0.330599
$320$	2.25948	+	2.25948i	0.126309	+	0.126309i
$321$		−	2.07568i		−	0.115853i
$322$	3.59740			0.200475
$323$	−21.8498	+	16.2991i	−1.21576	+	0.906907i
$324$	−8.89255			−0.494031
$325$		−	0.368117i		−	0.0204195i
$326$	−7.90604	−	7.90604i	−0.437875	−	0.437875i
$327$	−6.56009			−0.362774
$328$	−13.7045	−	13.7045i	−0.756706	−	0.756706i
$329$	−6.56163	+	6.56163i	−0.361754	+	0.361754i
$330$	−0.771154	+	0.771154i	−0.0424507	+	0.0424507i
$331$		−	29.7637i		−	1.63596i	−0.575246	−	0.817981i	$-0.695094\pi$
$331$		−	29.7637i		−	1.63596i	0.575246	−	0.817981i	$-0.304906\pi$
$332$		−	5.53242i		−	0.303631i
$333$	6.07145	−	6.07145i	0.332714	−	0.332714i
$334$	0.123174	−	0.123174i	0.00673977	−	0.00673977i
$335$	5.61842	+	5.61842i	0.306967	+	0.306967i
$336$	−0.449361			−0.0245147
$337$	7.58826	+	7.58826i	0.413359	+	0.413359i	0.882907	−	0.469548i	$-0.155583\pi$
$337$	7.58826	+	7.58826i	0.413359	+	0.413359i	−0.469548	+	0.882907i	$0.655583\pi$
$338$		−	10.0790i		−	0.548226i
$339$	8.98224			0.487848
$340$	−0.822920	+	5.65575i	−0.0446291	+	0.306726i
$341$	−16.9223			−0.916393
$342$		−	14.0012i		−	0.757096i
$343$	−10.5783	−	10.5783i	−0.571175	−	0.571175i
$344$	−18.1026			−0.976026
$345$	1.48880	+	1.48880i	0.0801542	+	0.0801542i
$346$	11.0770	−	11.0770i	0.595504	−	0.595504i
$347$	0.809045	−	0.809045i	0.0434318	−	0.0434318i	−0.685057	−	0.728489i	$-0.740223\pi$
$347$	0.809045	−	0.809045i	0.0434318	−	0.0434318i	0.728489	+	0.685057i	$0.240223\pi$
$348$		−	1.74637i		−	0.0936153i
$349$			18.6531i			0.998476i	0.866465	+	0.499238i	$0.166387\pi$
$349$			18.6531i			0.998476i	−0.866465	+	0.499238i	$0.833613\pi$
$350$	0.658417	−	0.658417i	0.0351939	−	0.0351939i
$351$	−0.809008	+	0.809008i	−0.0431816	+	0.0431816i
$352$	−10.5647	−	10.5647i	−0.563102	−	0.563102i
$353$	4.34305			0.231157			0.115579	−	0.993298i	$-0.463128\pi$
$353$	4.34305			0.231157			0.115579	+	0.993298i	$0.463128\pi$
$354$	−1.57716	−	1.57716i	−0.0838250	−	0.0838250i
$355$		−	11.8880i		−	0.630951i
$356$	12.6739			0.671714
$357$	1.59676	+	2.14055i	0.0845096	+	0.113290i
$358$	19.0478			1.00671
$359$			6.35821i			0.335573i	0.985823	+	0.167787i	$0.0536620\pi$
$359$			6.35821i			0.335573i	−0.985823	+	0.167787i	$0.946338\pi$
$360$	−5.07066	−	5.07066i	−0.267247	−	0.267247i
$361$	−24.7104			−1.30055
$362$	6.58517	+	6.58517i	0.346109	+	0.346109i
$363$	−1.72490	+	1.72490i	−0.0905339	+	0.0905339i
$364$	0.428822	−	0.428822i	0.0224764	−	0.0224764i
$365$			14.7327i			0.771147i
$366$			3.46762i			0.181256i
$367$	−11.4655	+	11.4655i	−0.598496	+	0.598496i	−0.939912	−	0.341416i	$-0.889093\pi$
$367$	−11.4655	+	11.4655i	−0.598496	+	0.598496i	0.341416	+	0.939912i	$0.389093\pi$
$368$	−1.89533	+	1.89533i	−0.0988009	+	0.0988009i
$369$	13.9629	+	13.9629i	0.726881	+	0.726881i
$370$	2.48878			0.129386
$371$	6.73329	+	6.73329i	0.349575	+	0.349575i
$372$			5.00494i			0.259494i
$373$	−18.5947			−0.962797			−0.481398	−	0.876502i	$-0.659871\pi$
$373$	−18.5947			−0.962797			−0.481398	+	0.876502i	$0.659871\pi$
$374$	−1.18801	+	8.16495i	−0.0614306	+	0.422200i
$375$	0.544977			0.0281425
$376$			20.7143i			1.06826i
$377$	0.601748	+	0.601748i	0.0309916	+	0.0309916i
$378$	−2.89399			−0.148851
$379$	−6.40722	−	6.40722i	−0.329117	−	0.329117i	0.523134	−	0.852251i	$-0.324763\pi$
$379$	−6.40722	−	6.40722i	−0.329117	−	0.329117i	−0.852251	+	0.523134i	$0.824763\pi$
$380$	−6.48026	+	6.48026i	−0.332430	+	0.332430i
$381$	1.72947	−	1.72947i	0.0886037	−	0.0886037i
$382$		−	13.5486i		−	0.693208i
$383$		−	2.75136i		−	0.140588i	−0.997526	−	0.0702941i	$-0.977606\pi$
$383$		−	2.75136i		−	0.140588i	0.997526	−	0.0702941i	$-0.0223938\pi$
$384$	−3.54356	+	3.54356i	−0.180832	+	0.180832i
$385$	−2.14649	+	2.14649i	−0.109395	+	0.109395i
$386$	1.00248	+	1.00248i	0.0510247	+	0.0510247i
$387$	18.4439			0.937557
$388$	−6.92430	−	6.92430i	−0.351528	−	0.351528i
$389$			27.3962i			1.38904i	0.719472	+	0.694521i	$0.244384\pi$
$389$			27.3962i			1.38904i	−0.719472	+	0.694521i	$0.755616\pi$
$390$	−0.157177			−0.00795898
$391$	15.7633	+	2.29359i	0.797187	+	0.115992i
$392$	−14.8236			−0.748704
$393$		−	5.09169i		−	0.256842i
$394$	9.18444	+	9.18444i	0.462705	+	0.462705i
$395$	−0.813189			−0.0409160
$396$	6.76705	+	6.76705i	0.340057	+	0.340057i
$397$	17.6654	−	17.6654i	0.886603	−	0.886603i	−0.107592	−	0.994195i	$-0.534314\pi$
$397$	17.6654	−	17.6654i	0.886603	−	0.886603i	0.994195	+	0.107592i	$0.0343139\pi$
$398$	13.9392	−	13.9392i	0.698710	−	0.698710i
$399$			4.28214i			0.214375i
$400$			0.693788i			0.0346894i
$401$	22.4405	−	22.4405i	1.12063	−	1.12063i	0.128978	−	0.991648i	$-0.458830\pi$
$401$	22.4405	−	22.4405i	1.12063	−	1.12063i	0.991648	−	0.128978i	$-0.0411695\pi$
$402$	2.39893	−	2.39893i	0.119648	−	0.119648i
$403$	−1.72456	−	1.72456i	−0.0859063	−	0.0859063i
$404$	0.410670			0.0204316
$405$	4.53624	+	4.53624i	0.225408	+	0.225408i
$406$			2.15258i			0.106831i
$407$	−8.11362			−0.402177
$408$	5.89912	+	0.858329i	0.292050	+	0.0424936i
$409$	0.721793			0.0356904			0.0178452	−	0.999841i	$-0.494319\pi$
$409$	0.721793			0.0356904			0.0178452	+	0.999841i	$0.494319\pi$
$410$			5.72362i			0.282670i
$411$	3.26714	+	3.26714i	0.161156	+	0.161156i
$412$	23.6164			1.16350
$413$	−4.38998	−	4.38998i	−0.216017	−	0.216017i
$414$	−5.78535	+	5.78535i	−0.284334	+	0.284334i
$415$	−2.82218	+	2.82218i	−0.138535	+	0.138535i
$416$		−	2.15331i		−	0.105575i
$417$		−	3.27369i		−	0.160313i
$418$	−9.35526	+	9.35526i	−0.457581	+	0.457581i
$419$	−10.1371	+	10.1371i	−0.495230	+	0.495230i	−0.909949	−	0.414719i	$-0.863880\pi$
$419$	−10.1371	+	10.1371i	−0.495230	+	0.495230i	0.414719	+	0.909949i	$0.363880\pi$
$420$	0.634847	+	0.634847i	0.0309773	+	0.0309773i
$421$	2.94304			0.143435			0.0717175	−	0.997425i	$-0.477152\pi$
$421$	2.94304			0.143435			0.0717175	+	0.997425i	$0.477152\pi$
$422$	4.65818	+	4.65818i	0.226757	+	0.226757i
$423$		−	21.1048i		−	1.02615i
$424$	21.2562			1.03229
$425$	3.30488	−	2.46531i	0.160310	−	0.119585i
$426$	−5.07590			−0.245928
$427$			9.65204i			0.467095i
$428$	−3.73320	−	3.73320i	−0.180451	−	0.180451i
$429$	0.512410			0.0247394
$430$	3.78022	+	3.78022i	0.182299	+	0.182299i
$431$	−22.7514	+	22.7514i	−1.09590	+	1.09590i	−0.101013	+	0.994885i	$0.532208\pi$
$431$	−22.7514	+	22.7514i	−1.09590	+	1.09590i	−0.994885	+	0.101013i	$0.967792\pi$
$432$	1.52473	−	1.52473i	0.0733586	−	0.0733586i
$433$		−	1.76074i		−	0.0846158i	−0.999105	−	0.0423079i	$-0.986529\pi$
$433$		−	1.76074i		−	0.0846158i	0.999105	−	0.0423079i	$-0.0134710\pi$
$434$		−	6.16911i		−	0.296127i
$435$	−0.890854	+	0.890854i	−0.0427132	+	0.0427132i
$436$	−11.7986	+	11.7986i	−0.565053	+	0.565053i
$437$	18.0614	+	18.0614i	0.863992	+	0.863992i
$438$	6.29052			0.300573
$439$	0.390096	+	0.390096i	0.0186183	+	0.0186183i	0.716355	−	0.697736i	$-0.245809\pi$
$439$	0.390096	+	0.390096i	0.0186183	+	0.0186183i	−0.697736	+	0.716355i	$0.745809\pi$
$440$			6.77621i			0.323043i
$441$	15.1031			0.719194
$442$	−0.953164	+	0.711023i	−0.0453374	+	0.0338199i
$443$	2.19117			0.104106			0.0520528	−	0.998644i	$-0.483424\pi$
$443$	2.19117			0.104106			0.0520528	+	0.998644i	$0.483424\pi$
$444$			2.39969i			0.113884i
$445$	−6.46516	−	6.46516i	−0.306478	−	0.306478i
$446$	−12.9665			−0.613980
$447$	3.51376	+	3.51376i	0.166195	+	0.166195i
$448$	2.68534	−	2.68534i	0.126870	−	0.126870i
$449$	1.52719	−	1.52719i	0.0720727	−	0.0720727i	−0.670152	−	0.742224i	$-0.733771\pi$
$449$	1.52719	−	1.52719i	0.0720727	−	0.0720727i	0.742224	+	0.670152i	$0.233771\pi$
$450$			2.11773i			0.0998310i
$451$		−	18.6594i		−	0.878639i
$452$	16.1550	−	16.1550i	0.759868	−	0.759868i
$453$	−5.05374	+	5.05374i	−0.237445	+	0.237445i
$454$	−3.94282	−	3.94282i	−0.185046	−	0.185046i
$455$	−0.437499			−0.0205103
$456$	6.75910	+	6.75910i	0.316524	+	0.316524i
$457$		−	9.46893i		−	0.442938i	−0.975167	−	0.221469i	$-0.928915\pi$
$457$		−	9.46893i		−	0.442938i	0.975167	−	0.221469i	$-0.0710851\pi$
$458$	1.14993			0.0537329
$459$	−12.6811	−	1.84512i	−0.591903	−	0.0861226i
$460$	5.35536			0.249695
$461$		−	16.6646i		−	0.776149i	−0.921628	−	0.388075i	$-0.873140\pi$
$461$		−	16.6646i		−	0.776149i	0.921628	−	0.388075i	$-0.126860\pi$
$462$	0.916499	+	0.916499i	0.0426394	+	0.0426394i
$463$	14.3738			0.668009			0.334005	−	0.942571i	$-0.391600\pi$
$463$	14.3738			0.668009			0.334005	+	0.942571i	$0.391600\pi$
$464$	−1.13411	−	1.13411i	−0.0526498	−	0.0526498i
$465$	2.55311	−	2.55311i	0.118397	−	0.118397i
$466$	−12.8341	+	12.8341i	−0.594530	+	0.594530i
$467$			12.9129i			0.597537i	0.954326	+	0.298769i	$0.0965759\pi$
$467$			12.9129i			0.597537i	−0.954326	+	0.298769i	$0.903424\pi$
$468$			1.37927i			0.0637565i
$469$	6.67736	−	6.67736i	0.308332	−	0.308332i
$470$	4.32560	−	4.32560i	0.199525	−	0.199525i
$471$	−7.72624	−	7.72624i	−0.356006	−	0.356006i
$472$	−13.8586			−0.637896
$473$	−12.3238	−	12.3238i	−0.566650	−	0.566650i
$474$			0.347212i			0.0159480i
$475$	6.61138			0.303351
$476$	6.72173	+	0.978021i	0.308090	+	0.0448275i
$477$	−21.6570			−0.991604
$478$		−	5.03972i		−	0.230511i
$479$	4.25108	+	4.25108i	0.194237	+	0.194237i	0.797524	−	0.603287i	$-0.206143\pi$
$479$	4.25108	+	4.25108i	0.194237	+	0.194237i	−0.603287	+	0.797524i	$0.706143\pi$
$480$	3.18785			0.145505
$481$	−0.826862	−	0.826862i	−0.0377017	−	0.0377017i
$482$	−15.1774	+	15.1774i	−0.691310	+	0.691310i
$483$	1.76940	−	1.76940i	0.0805106	−	0.0805106i
$484$			6.20464i			0.282029i
$485$			7.06440i			0.320778i
$486$	7.10237	−	7.10237i	0.322170	−	0.322170i
$487$	23.4059	−	23.4059i	1.06062	−	1.06062i	0.0625852	−	0.998040i	$-0.480065\pi$
$487$	23.4059	−	23.4059i	1.06062	−	1.06062i	0.998040	−	0.0625852i	$-0.0199345\pi$
$488$	15.2352	+	15.2352i	0.689664	+	0.689664i
$489$	−7.77725			−0.351699
$490$	3.09549	+	3.09549i	0.139840	+	0.139840i
$491$		−	18.7705i		−	0.847099i	−0.905873	−	0.423549i	$-0.860784\pi$
$491$		−	18.7705i		−	0.847099i	0.905873	−	0.423549i	$-0.139216\pi$
$492$	−5.51872			−0.248803
$493$	−1.37242	+	9.43233i	−0.0618105	+	0.424811i
$494$	−1.90680			−0.0857908
$495$		−	6.90397i		−	0.310311i
$496$	3.25026	+	3.25026i	0.145941	+	0.145941i
$497$	−14.1286			−0.633756
$498$	1.20500	+	1.20500i	0.0539974	+	0.0539974i
$499$	−5.05185	+	5.05185i	−0.226152	+	0.226152i	−0.811083	−	0.584931i	$-0.801122\pi$
$499$	−5.05185	+	5.05185i	−0.226152	+	0.226152i	0.584931	+	0.811083i	$0.301122\pi$
$500$	0.980167	−	0.980167i	0.0438344	−	0.0438344i
$501$		−	0.121167i		−	0.00541336i
$502$			0.183657i			0.00819700i
$503$	−20.7561	+	20.7561i	−0.925467	+	0.925467i	−0.997409	−	0.0719417i	$-0.977080\pi$
$503$	−20.7561	+	20.7561i	−0.925467	+	0.925467i	0.0719417	+	0.997409i	$0.477080\pi$
$504$	−6.02637	+	6.02637i	−0.268436	+	0.268436i
$505$	−0.209490	−	0.209490i	−0.00932216	−	0.00932216i
$506$	7.73128			0.343697
$507$	−4.95742	−	4.95742i	−0.220167	−	0.220167i
$508$		−	6.22109i		−	0.276016i
$509$	−9.83824			−0.436072			−0.218036	−	0.975941i	$-0.569965\pi$
$509$	−9.83824			−0.436072			−0.218036	+	0.975941i	$0.569965\pi$
$510$	−1.05263	−	1.41110i	−0.0466112	−	0.0624848i
$511$	17.5095			0.774575
$512$			7.73954i			0.342043i
$513$	−14.5298	−	14.5298i	−0.641505	−	0.641505i
$514$	−2.78949			−0.123039
$515$	−12.0471	−	12.0471i	−0.530860	−	0.530860i
$516$	−3.64490	+	3.64490i	−0.160458	+	0.160458i
$517$	−14.1018	+	14.1018i	−0.620195	+	0.620195i
$518$		−	2.95786i		−	0.129961i
$519$		−	10.8966i		−	0.478307i
$520$	−0.690566	+	0.690566i	−0.0302833	+	0.0302833i
$521$	−4.82486	+	4.82486i	−0.211381	+	0.211381i	−0.804854	−	0.593473i	$-0.797756\pi$
$521$	−4.82486	+	4.82486i	−0.211381	+	0.211381i	0.593473	+	0.804854i	$0.297756\pi$
$522$	−3.46178	−	3.46178i	−0.151518	−	0.151518i
$523$	−7.90422			−0.345628			−0.172814	−	0.984955i	$-0.555286\pi$
$523$	−7.90422			−0.345628			−0.172814	+	0.984955i	$0.555286\pi$
$524$	−9.15766	−	9.15766i	−0.400054	−	0.400054i
$525$		−	0.647692i		−	0.0282676i
$526$	−23.5043			−1.02484
$527$	3.93322	−	27.0322i	0.171334	−	1.17754i
$528$	−0.965735			−0.0420282
$529$			8.07391i			0.351040i
$530$	−4.43876	−	4.43876i	−0.192807	−	0.192807i
$531$	14.1199			0.612754
$532$	7.70164	+	7.70164i	0.333908	+	0.333908i
$533$	1.90159	−	1.90159i	0.0823670	−	0.0823670i
$534$	−2.76047	+	2.76047i	−0.119457	+	0.119457i
$535$			3.80874i			0.164666i
$536$		−	21.0796i		−	0.910501i
$537$	9.36878	−	9.36878i	0.404293	−	0.404293i
$538$	0.210101	−	0.210101i	0.00905809	−	0.00905809i
$539$	−10.0915	−	10.0915i	−0.434673	−	0.434673i
$540$	−4.30821			−0.185396
$541$	−25.6567	−	25.6567i	−1.10307	−	1.10307i	−0.994039	−	0.109027i	$-0.965226\pi$
$541$	−25.6567	−	25.6567i	−1.10307	−	1.10307i	−0.109027	−	0.994039i	$-0.534774\pi$
$542$			8.31614i			0.357209i
$543$	6.47790			0.277993
$544$	19.3320	−	14.4209i	0.828852	−	0.618291i
$545$	12.0374			0.515625
$546$			0.186802i			0.00799437i
$547$	19.9968	+	19.9968i	0.855002	+	0.855002i	0.990744	−	0.135742i	$-0.0433420\pi$
$547$	19.9968	+	19.9968i	0.855002	+	0.855002i	−0.135742	+	0.990744i	$0.543342\pi$
$548$	11.7522			0.502030
$549$	−15.5224	−	15.5224i	−0.662481	−	0.662481i
$550$	1.41502	−	1.41502i	0.0603368	−	0.0603368i
$551$	−10.8074	+	10.8074i	−0.460410	+	0.460410i
$552$		−	5.58579i		−	0.237747i
$553$			0.966456i			0.0410979i
$554$	−16.8928	+	16.8928i	−0.717708	+	0.717708i
$555$	1.22412	−	1.22412i	0.0519611	−	0.0519611i
$556$	−5.88789	−	5.88789i	−0.249702	−	0.249702i
$557$	−15.4059			−0.652768			−0.326384	−	0.945237i	$-0.605830\pi$
$557$	−15.4059			−0.652768			−0.326384	+	0.945237i	$0.605830\pi$
$558$	9.92116	+	9.92116i	0.419996	+	0.419996i
$559$		−	2.51185i		−	0.106240i
$560$	0.824551			0.0348437
$561$	3.43165	+	4.60031i	0.144884	+	0.194225i
$562$	20.7153			0.873820
$563$		−	8.51617i		−	0.358914i	−0.983766	−	0.179457i	$-0.942566\pi$
$563$		−	8.51617i		−	0.358914i	0.983766	−	0.179457i	$-0.0574340\pi$
$564$	4.17075	+	4.17075i	0.175620	+	0.175620i
$565$	−16.4819			−0.693398
$566$	10.2912	+	10.2912i	0.432571	+	0.432571i
$567$	5.39122	−	5.39122i	0.226410	−	0.226410i
$568$	−22.3012	+	22.3012i	−0.935738	+	0.935738i
$569$		−	10.0268i		−	0.420346i	−0.977664	−	0.210173i	$-0.932597\pi$
$569$		−	10.0268i		−	0.420346i	0.977664	−	0.210173i	$-0.0674027\pi$
$570$		−	2.82290i		−	0.118238i
$571$	−9.77041	+	9.77041i	−0.408879	+	0.408879i	−0.881347	−	0.472469i	$-0.843363\pi$
$571$	−9.77041	+	9.77041i	−0.408879	+	0.408879i	0.472469	+	0.881347i	$0.343363\pi$
$572$	0.921594	−	0.921594i	0.0385338	−	0.0385338i
$573$	−6.66396	−	6.66396i	−0.278391	−	0.278391i
$574$	6.80239			0.283926
$575$	−2.73186	−	2.73186i	−0.113926	−	0.113926i
$576$			8.63712i			0.359880i
$577$	−13.6068			−0.566457			−0.283229	−	0.959052i	$-0.591406\pi$
$577$	−13.6068			−0.566457			−0.283229	+	0.959052i	$0.591406\pi$
$578$	−12.7668	−	3.79554i	−0.531030	−	0.157873i
$579$	0.986147			0.0409829
$580$			3.20449i			0.133059i
$581$	3.35409	+	3.35409i	0.139151	+	0.139151i
$582$	3.01633			0.125031
$583$	14.4707	+	14.4707i	0.599315	+	0.599315i
$584$	27.6377	−	27.6377i	1.14366	−	1.14366i
$585$	0.703586	−	0.703586i	0.0290897	−	0.0290897i
$586$			2.82018i			0.116501i
$587$			27.9191i			1.15234i	0.817329	+	0.576172i	$0.195454\pi$
$587$			27.9191i			1.15234i	−0.817329	+	0.576172i	$0.804546\pi$
$588$	−2.98468	+	2.98468i	−0.123086	+	0.123086i
$589$	30.9730	−	30.9730i	1.27622	−	1.27622i
$590$	2.89399	+	2.89399i	0.119144	+	0.119144i
$591$	9.03483			0.371643
$592$	1.55838	+	1.55838i	0.0640491	+	0.0640491i
$593$			40.0318i			1.64391i	0.569554	+	0.821954i	$0.307116\pi$
$593$			40.0318i			1.64391i	−0.569554	+	0.821954i	$0.692884\pi$
$594$	−6.21956			−0.255192
$595$	−2.92996	−	3.92778i	−0.120117	−	0.161023i
$596$	12.6394			0.517728
$597$		−	13.7122i		−	0.561201i
$598$	0.787898	+	0.787898i	0.0322195	+	0.0322195i
$599$	25.5481			1.04387			0.521934	−	0.852986i	$-0.325211\pi$
$599$	25.5481			1.04387			0.521934	+	0.852986i	$0.325211\pi$
$600$	−1.02234	−	1.02234i	−0.0417370	−	0.0417370i
$601$	2.75133	−	2.75133i	0.112229	−	0.112229i	−0.648762	−	0.760991i	$-0.724713\pi$
$601$	2.75133	−	2.75133i	0.112229	−	0.112229i	0.760991	+	0.648762i	$0.224713\pi$
$602$	4.49271	−	4.49271i	0.183109	−	0.183109i
$603$			21.4771i			0.874614i
$604$			18.1788i			0.739684i
$605$	3.16509	−	3.16509i	0.128679	−	0.128679i
$606$	−0.0894470	+	0.0894470i	−0.00363353	+	0.00363353i
$607$	−6.94385	−	6.94385i	−0.281842	−	0.281842i	0.552001	−	0.833843i	$-0.313864\pi$
$607$	−6.94385	−	6.94385i	−0.281842	−	0.281842i	−0.833843	+	0.552001i	$0.813864\pi$
$608$	38.6734			1.56841
$609$	1.05876	+	1.05876i	0.0429031	+	0.0429031i
$610$		−	6.36288i		−	0.257626i
$611$	−2.87423			−0.116279
$612$	−12.3828	+	9.23705i	−0.500543	+	0.373385i
$613$	44.6175			1.80208			0.901042	−	0.433733i	$-0.142804\pi$
$613$	44.6175			1.80208			0.901042	+	0.433733i	$0.142804\pi$
$614$		−	26.1781i		−	1.05646i
$615$	2.81519	+	2.81519i	0.113520	+	0.113520i
$616$	8.05337			0.324479
$617$	−25.2341	−	25.2341i	−1.01589	−	1.01589i	−0.999872	−	0.0160159i	$-0.994902\pi$
$617$	−25.2341	−	25.2341i	−1.01589	−	1.01589i	−0.0160159	−	0.999872i	$-0.505098\pi$
$618$	−5.14383	+	5.14383i	−0.206915	+	0.206915i
$619$	−11.7276	+	11.7276i	−0.471371	+	0.471371i	−0.902358	−	0.430987i	$-0.858166\pi$
$619$	−11.7276	+	11.7276i	−0.471371	+	0.471371i	0.430987	+	0.902358i	$0.358166\pi$
$620$		−	9.18378i		−	0.368829i
$621$			12.0075i			0.481846i
$622$	−7.64303	+	7.64303i	−0.306458	+	0.306458i
$623$	−7.68369	+	7.68369i	−0.307841	+	0.307841i
$624$	−0.0984184	−	0.0984184i	−0.00393989	−	0.00393989i
$625$	−1.00000			−0.0400000
$626$	16.9359	+	16.9359i	0.676897	+	0.676897i
$627$			9.20287i			0.367527i
$628$	−27.7920			−1.10902
$629$	1.88584	−	12.9610i	0.0751932	−	0.516787i
$630$	2.51688			0.100275
$631$			38.0364i			1.51421i	0.653295	+	0.757103i	$0.273386\pi$
$631$			38.0364i			1.51421i	−0.653295	+	0.757103i	$0.726614\pi$
$632$	1.52549	+	1.52549i	0.0606808	+	0.0606808i
$633$	4.58231			0.182130
$634$	−1.78222	−	1.78222i	−0.0707811	−	0.0707811i
$635$	−3.17348	+	3.17348i	−0.125936	+	0.125936i
$636$	4.27986	−	4.27986i	0.169707	−	0.169707i
$637$		−	2.05686i		−	0.0814959i
$638$			4.62617i			0.183152i
$639$	22.7217	−	22.7217i	0.898857	−	0.898857i
$640$	6.50223	−	6.50223i	0.257023	−	0.257023i
$641$	2.57412	+	2.57412i	0.101672	+	0.101672i	0.756113	−	0.654441i	$-0.227096\pi$
$641$	2.57412	+	2.57412i	0.101672	+	0.101672i	−0.654441	+	0.756113i	$0.727096\pi$
$642$	1.62624			0.0641826
$643$	13.0129	+	13.0129i	0.513178	+	0.513178i	0.915499	−	0.402321i	$-0.131796\pi$
$643$	13.0129	+	13.0129i	0.513178	+	0.513178i	−0.402321	+	0.915499i	$0.631796\pi$
$644$		−	6.36472i		−	0.250805i
$645$	3.71865			0.146422
$646$	−12.7700	−	17.1188i	−0.502427	−	0.673531i
$647$	3.12579			0.122888			0.0614438	−	0.998111i	$-0.480429\pi$
$647$	3.12579			0.122888			0.0614438	+	0.998111i	$0.480429\pi$
$648$		−	17.0194i		−	0.668586i
$649$	−9.43463	−	9.43463i	−0.370342	−	0.370342i
$650$	0.288411			0.0113124
$651$	−3.03431	−	3.03431i	−0.118924	−	0.118924i
$652$	−13.9878	+	13.9878i	−0.547803	+	0.547803i
$653$	9.92621	−	9.92621i	0.388443	−	0.388443i	−0.485689	−	0.874132i	$-0.661431\pi$
$653$	9.92621	−	9.92621i	0.388443	−	0.388443i	0.874132	+	0.485689i	$0.161431\pi$
$654$		−	5.13967i		−	0.200977i
$655$			9.34295i			0.365059i
$656$	−3.58391	+	3.58391i	−0.139928	+	0.139928i
$657$	−28.1588	+	28.1588i	−1.09858	+	1.09858i
$658$	−5.14087	−	5.14087i	−0.200412	−	0.200412i
$659$	4.52370			0.176218			0.0881092	−	0.996111i	$-0.471918\pi$
$659$	4.52370			0.176218			0.0881092	+	0.996111i	$0.471918\pi$
$660$	1.36437	+	1.36437i	0.0531079	+	0.0531079i
$661$			31.6484i			1.23098i	0.788145	+	0.615490i	$0.211042\pi$
$661$			31.6484i			1.23098i	−0.788145	+	0.615490i	$0.788958\pi$
$662$	23.3191			0.906324
$663$	−0.119099	+	0.818539i	−0.00462540	+	0.0317894i
$664$	10.5885			0.410912
$665$		−	7.85747i		−	0.304700i
$666$	4.75684	+	4.75684i	0.184324	+	0.184324i
$667$	8.93134			0.345823
$668$	−0.217925	−	0.217925i	−0.00843179	−	0.00843179i
$669$	−6.37762	+	6.37762i	−0.246573	+	0.246573i
$670$	−4.40189	+	4.40189i	−0.170060	+	0.170060i
$671$			20.7435i			0.800793i
$672$		−	3.78869i		−	0.146152i
$673$	−7.91436	+	7.91436i	−0.305076	+	0.305076i	−0.842996	−	0.537920i	$-0.819210\pi$
$673$	−7.91436	+	7.91436i	−0.305076	+	0.305076i	0.537920	+	0.842996i	$0.319210\pi$
$674$	−5.94522	+	5.94522i	−0.229001	+	0.229001i
$675$	2.19769	+	2.19769i	0.0845891	+	0.0845891i
$676$	−17.8323			−0.685858
$677$	−4.61971	−	4.61971i	−0.177550	−	0.177550i	0.612737	−	0.790287i	$-0.290069\pi$
$677$	−4.61971	−	4.61971i	−0.177550	−	0.177550i	−0.790287	+	0.612737i	$0.790069\pi$
$678$			7.03737i			0.270268i
$679$	8.39588			0.322204
$680$	−10.8245	−	1.57498i	−0.415102	−	0.0603979i
$681$	−3.87860			−0.148628
$682$		−	13.2582i		−	0.507683i
$683$	16.7322	+	16.7322i	0.640239	+	0.640239i	0.950614	−	0.310376i	$-0.100455\pi$
$683$	16.7322	+	16.7322i	0.640239	+	0.640239i	−0.310376	+	0.950614i	$0.600455\pi$
$684$	−24.7716			−0.947165
$685$	−5.99501	−	5.99501i	−0.229058	−	0.229058i
$686$	8.28784	−	8.28784i	0.316431	−	0.316431i
$687$	0.565602	−	0.565602i	0.0215790	−	0.0215790i
$688$			4.73406i			0.180484i
$689$			2.94943i			0.112364i
$690$	−1.16644	+	1.16644i	−0.0444055	+	0.0444055i
$691$	−5.73536	+	5.73536i	−0.218183	+	0.218183i	−0.807732	−	0.589549i	$-0.799305\pi$
$691$	−5.73536	+	5.73536i	−0.218183	+	0.218183i	0.589549	+	0.807732i	$0.299305\pi$
$692$	−19.5980	−	19.5980i	−0.745006	−	0.745006i
$693$	−8.20521			−0.311690
$694$	0.633867	+	0.633867i	0.0240613	+	0.0240613i
$695$			6.00703i			0.227859i
$696$	3.34237			0.126692
$697$	29.8072	+	4.33698i	1.12903	+	0.164275i
$698$	−14.6142			−0.553157
$699$			12.6251i			0.477525i
$700$	−1.16491	−	1.16491i	−0.0440293	−	0.0440293i
$701$	35.4115			1.33748			0.668738	−	0.743498i	$-0.266835\pi$
$701$	35.4115			1.33748			0.668738	+	0.743498i	$0.266835\pi$
$702$	−0.633838	−	0.633838i	−0.0239227	−	0.0239227i
$703$	14.8504	−	14.8504i	0.560094	−	0.560094i
$704$	5.77113	−	5.77113i	0.217508	−	0.217508i
$705$		−	4.25514i		−	0.160258i
$706$			3.40268i			0.128061i
$707$	−0.248973	+	0.248973i	−0.00936361	+	0.00936361i
$708$	−2.79039	+	2.79039i	−0.104869	+	0.104869i
$709$	−10.5641	−	10.5641i	−0.396745	−	0.396745i	0.480338	−	0.877083i	$-0.340514\pi$
$709$	−10.5641	−	10.5641i	−0.396745	−	0.396745i	−0.877083	+	0.480338i	$0.840514\pi$
$710$	9.31398			0.349547
$711$	−1.55426	−	1.55426i	−0.0582891	−	0.0582891i
$712$			24.2565i			0.909050i
$713$	−25.5964			−0.958593
$714$	−1.67707	+	1.25102i	−0.0627626	+	0.0468184i
$715$	−0.940241			−0.0351630
$716$		−	33.7004i		−	1.25944i
$717$	−2.47881	−	2.47881i	−0.0925730	−	0.0925730i
$718$	−4.98150			−0.185908
$719$	−16.3734	−	16.3734i	−0.610624	−	0.610624i	0.332485	−	0.943109i	$-0.392113\pi$
$719$	−16.3734	−	16.3734i	−0.610624	−	0.610624i	−0.943109	+	0.332485i	$0.892113\pi$
$720$	−1.32604	+	1.32604i	−0.0494188	+	0.0494188i
$721$	−14.3177	+	14.3177i	−0.533220	+	0.533220i
$722$		−	19.3600i		−	0.720504i
$723$			14.9301i			0.555258i
$724$	11.6508	−	11.6508i	0.433000	−	0.433000i
$725$	1.63466	−	1.63466i	0.0607099	−	0.0607099i
$726$	−1.35142	−	1.35142i	−0.0501559	−	0.0501559i
$727$	11.3367			0.420456			0.210228	−	0.977652i	$-0.432579\pi$
$727$	11.3367			0.420456			0.210228	+	0.977652i	$0.432579\pi$
$728$	0.820721	+	0.820721i	0.0304180	+	0.0304180i
$729$			12.2590i			0.454036i
$730$	−11.5427			−0.427216
$731$	22.5509	−	16.8220i	0.834074	−	0.622186i
$732$	6.13510			0.226760
$733$		−	3.32332i		−	0.122750i	−0.998115	−	0.0613748i	$-0.980452\pi$
$733$		−	3.32332i		−	0.122750i	0.998115	−	0.0613748i	$-0.0195485\pi$
$734$	−8.98296	−	8.98296i	−0.331567	−	0.331567i
$735$	3.04507			0.112319
$736$	−15.9801	−	15.9801i	−0.589033	−	0.589033i
$737$	14.3505	−	14.3505i	0.528607	−	0.528607i
$738$	−10.9396	+	10.9396i	−0.402693	+	0.402693i
$739$		−	12.5661i		−	0.462253i	−0.972924	−	0.231127i	$-0.925759\pi$
$739$		−	12.5661i		−	0.462253i	0.972924	−	0.231127i	$-0.0742412\pi$
$740$		−	4.40329i		−	0.161868i
$741$	−0.937867	+	0.937867i	−0.0344534	+	0.0344534i
$742$	−5.27537	+	5.27537i	−0.193665	+	0.193665i
$743$	−37.1805	−	37.1805i	−1.36402	−	1.36402i	−0.868724	−	0.495297i	$-0.835059\pi$
$743$	−37.1805	−	37.1805i	−1.36402	−	1.36402i	−0.495297	−	0.868724i	$-0.664941\pi$
$744$	−9.57894			−0.351181
$745$	−6.44755	−	6.44755i	−0.236220	−	0.236220i
$746$		−	14.5685i		−	0.533390i
$747$	−10.7881			−0.394717
$748$	14.4459	+	2.10189i	0.528193	+	0.0768528i
$749$	4.52660			0.165398
$750$			0.426976i			0.0155910i
$751$	2.78545	+	2.78545i	0.101642	+	0.101642i	0.756099	−	0.654457i	$-0.227103\pi$
$751$	2.78545	+	2.78545i	0.101642	+	0.101642i	−0.654457	+	0.756099i	$0.727103\pi$
$752$	5.41705			0.197539
$753$	0.0903325	+	0.0903325i	0.00329190	+	0.00329190i
$754$	−0.471455	+	0.471455i	−0.0171694	+	0.0171694i
$755$	9.27331	−	9.27331i	0.337490	−	0.337490i
$756$			5.12020i			0.186220i
$757$		−	6.38475i		−	0.232058i	−0.993246	−	0.116029i	$-0.962984\pi$
$757$		−	6.38475i		−	0.232058i	0.993246	−	0.116029i	$-0.0370165\pi$
$758$	5.01990	−	5.01990i	0.182331	−	0.182331i
$759$	3.80267	−	3.80267i	0.138028	−	0.138028i
$760$	−12.4025	−	12.4025i	−0.449888	−	0.449888i
$761$	−19.3638			−0.701938			−0.350969	−	0.936387i	$-0.614148\pi$
$761$	−19.3638			−0.701938			−0.350969	+	0.936387i	$0.614148\pi$
$762$	1.35500	+	1.35500i	0.0490865	+	0.0490865i
$763$		−	14.3061i		−	0.517917i
$764$	−23.9709			−0.867238
$765$	11.0286	+	1.60468i	0.398741	+	0.0580173i
$766$	2.15563			0.0778860
$767$		−	1.92297i		−	0.0694346i
$768$	−5.23902	−	5.23902i	−0.189047	−	0.189047i
$769$	5.10469			0.184080			0.0920398	−	0.995755i	$-0.470661\pi$
$769$	5.10469			0.184080			0.0920398	+	0.995755i	$0.470661\pi$
$770$	−1.68172	−	1.68172i	−0.0606051	−	0.0606051i
$771$	−1.37203	+	1.37203i	−0.0494123	+	0.0494123i
$772$	1.77363	−	1.77363i	0.0638345	−	0.0638345i
$773$		−	3.00249i		−	0.107992i	−0.998541	−	0.0539961i	$-0.982804\pi$
$773$		−	3.00249i		−	0.107992i	0.998541	−	0.0539961i	$-0.0171958\pi$
$774$			14.4504i			0.519408i
$775$	−4.68480	+	4.68480i	−0.168283	+	0.168283i
$776$	13.2524	−	13.2524i	0.475733	−	0.475733i
$777$	−1.45484	−	1.45484i	−0.0521921	−	0.0521921i
$778$	−21.4642			−0.769531
$779$	34.1525	+	34.1525i	1.22364	+	1.22364i
$780$			0.278086i			0.00995708i
$781$	−30.3643			−1.08652
$782$	−1.79697	+	12.3502i	−0.0642595	+	0.441642i
$783$	−7.18497			−0.256770
$784$			3.87656i			0.138448i
$785$	14.1772	+	14.1772i	0.506006	+	0.506006i
$786$	3.98921			0.142291
$787$	−1.86293	−	1.86293i	−0.0664063	−	0.0664063i	0.673124	−	0.739530i	$-0.264952\pi$
$787$	−1.86293	−	1.86293i	−0.0664063	−	0.0664063i	−0.739530	+	0.673124i	$0.764952\pi$
$788$	16.2496	−	16.2496i	0.578868	−	0.578868i
$789$	−11.5607	+	11.5607i	−0.411572	+	0.411572i
$790$		−	0.637113i		−	0.0226675i
$791$			19.5883i			0.696481i
$792$	−12.9514	+	12.9514i	−0.460209	+	0.460209i
$793$	−2.11398	+	2.11398i	−0.0750695	+	0.0750695i
$794$	13.8404	+	13.8404i	0.491179	+	0.491179i
$795$	−4.36646			−0.154862
$796$	−24.6620	−	24.6620i	−0.874121	−	0.874121i
$797$		−	27.2441i		−	0.965036i	−0.875886	−	0.482518i	$-0.839722\pi$
$797$		−	27.2441i		−	0.965036i	0.875886	−	0.482518i	$-0.160278\pi$
$798$	−3.35495			−0.118764
$799$	−19.2490	−	25.8043i	−0.680979	−	0.912890i
$800$	−5.84952			−0.206812
$801$		−	24.7138i		−	0.873221i
$802$	17.5816	+	17.5816i	0.620827	+	0.620827i
$803$	37.6302			1.32794
$804$	−4.24431	−	4.24431i	−0.149685	−	0.149685i
$805$	−3.24675	+	3.24675i	−0.114433	+	0.114433i
$806$	1.35115	−	1.35115i	0.0475921	−	0.0475921i
$807$		−	0.206679i		−	0.00727543i
$808$			0.785979i			0.0276506i
$809$	26.0978	−	26.0978i	0.917549	−	0.917549i	−0.0793013	−	0.996851i	$-0.525269\pi$
$809$	26.0978	−	26.0978i	0.917549	−	0.917549i	0.996851	+	0.0793013i	$0.0252689\pi$
$810$	−3.55403	+	3.55403i	−0.124876	+	0.124876i
$811$	−11.9007	−	11.9007i	−0.417891	−	0.417891i	0.466585	−	0.884476i	$-0.345484\pi$
$811$	−11.9007	−	11.9007i	−0.417891	−	0.417891i	−0.884476	+	0.466585i	$0.845484\pi$
$812$	3.80846			0.133651
$813$	4.09034	+	4.09034i	0.143454	+	0.143454i
$814$		−	6.35682i		−	0.222807i
$815$	14.2708			0.499884
$816$	0.224464	−	1.54270i	0.00785782	−	0.0540051i
$817$	45.1128			1.57830
$818$			0.565507i			0.0197725i
$819$	−0.836196	−	0.836196i	−0.0292191	−	0.0292191i
$820$	10.1265			0.353634
$821$	12.4565	+	12.4565i	0.434737	+	0.434737i	0.890236	−	0.455500i	$-0.150539\pi$
$821$	12.4565	+	12.4565i	0.434737	+	0.434737i	−0.455500	+	0.890236i	$0.650539\pi$
$822$	−2.55972	+	2.55972i	−0.0892806	+	0.0892806i
$823$	−20.8831	+	20.8831i	−0.727940	+	0.727940i	−0.970209	−	0.242269i	$-0.922108\pi$
$823$	−20.8831	+	20.8831i	−0.727940	+	0.727940i	0.242269	+	0.970209i	$0.422108\pi$
$824$			45.1994i			1.57459i
$825$		−	1.39197i		−	0.0484623i
$826$	3.43944	−	3.43944i	0.119674	−	0.119674i
$827$	−21.0943	+	21.0943i	−0.733521	+	0.733521i	−0.971316	−	0.237794i	$-0.923576\pi$
$827$	−21.0943	+	21.0943i	−0.733521	+	0.733521i	0.237794	+	0.971316i	$0.423576\pi$
$828$	10.2357	+	10.2357i	0.355717	+	0.355717i
$829$	−53.2461			−1.84931			−0.924657	−	0.380802i	$-0.875648\pi$
$829$	−53.2461			−1.84931			−0.924657	+	0.380802i	$0.875648\pi$
$830$	−2.21111	−	2.21111i	−0.0767487	−	0.0767487i
$831$			16.6177i			0.576461i
$832$	1.17628			0.0407800
$833$	18.4661	−	13.7750i	0.639812	−	0.477275i
$834$	2.56486			0.0888137
$835$			0.222335i			0.00769422i
$836$	16.5518	+	16.5518i	0.572456	+	0.572456i
$837$	20.5915			0.711745
$838$	−7.94217	−	7.94217i	−0.274358	−	0.274358i
$839$	−27.0544	+	27.0544i	−0.934022	+	0.934022i	−0.997954	−	0.0639326i	$-0.979636\pi$
$839$	−27.0544	+	27.0544i	−0.934022	+	0.934022i	0.0639326	+	0.997954i	$0.479636\pi$
$840$	−1.21503	+	1.21503i	−0.0419225	+	0.0419225i
$841$		−	23.6557i		−	0.815715i
$842$			2.30580i			0.0794632i
$843$	10.1889	−	10.1889i	0.350925	−	0.350925i
$844$	8.24150	−	8.24150i	0.283684	−	0.283684i
$845$	9.09657	+	9.09657i	0.312931	+	0.312931i
$846$	16.5351			0.568489
$847$	−3.76164	−	3.76164i	−0.129252	−	0.129252i
$848$		−	5.55876i		−	0.190889i
$849$	10.1236			0.347439
$850$	1.93151	+	2.58929i	0.0662503	+	0.0888121i
$851$	−12.2725			−0.420697
$852$			8.98055i			0.307668i
$853$	−4.75362	−	4.75362i	−0.162761	−	0.162761i	0.621028	−	0.783789i	$-0.286715\pi$
$853$	−4.75362	−	4.75362i	−0.162761	−	0.162761i	−0.783789	+	0.621028i	$0.786715\pi$
$854$	−7.56214			−0.258771
$855$	12.6364	+	12.6364i	0.432156	+	0.432156i
$856$	7.14497	−	7.14497i	0.244210	−	0.244210i
$857$	−22.7593	+	22.7593i	−0.777442	+	0.777442i	−0.979395	−	0.201953i	$-0.935271\pi$
$857$	−22.7593	+	22.7593i	−0.777442	+	0.777442i	0.201953	+	0.979395i	$0.435271\pi$
$858$			0.401460i			0.0137056i
$859$			46.6741i			1.59250i	0.604968	+	0.796250i	$0.293186\pi$
$859$			46.6741i			1.59250i	−0.604968	+	0.796250i	$0.706814\pi$
$860$	6.68817	−	6.68817i	0.228065	−	0.228065i
$861$	3.34579	−	3.34579i	0.114024	−	0.114024i
$862$	−17.8252	−	17.8252i	−0.607129	−	0.607129i
$863$	9.97544			0.339568			0.169784	−	0.985481i	$-0.445693\pi$
$863$	9.97544			0.339568			0.169784	+	0.985481i	$0.445693\pi$
$864$	12.8554	+	12.8554i	0.437351	+	0.437351i
$865$			19.9946i			0.679836i
$866$	1.37950			0.0468772
$867$	−8.14629	+	4.41258i	−0.276662	+	0.149859i
$868$	−10.9147			−0.370469
$869$			2.07704i			0.0704587i
$870$	−0.697962	−	0.697962i	−0.0236631	−	0.0236631i
$871$	2.92493			0.0991074
$872$	−22.5814	−	22.5814i	−0.764702	−	0.764702i
$873$	−13.5023	+	13.5023i	−0.456982	+	0.456982i
$874$	−14.1506	+	14.1506i	−0.478652	+	0.478652i
$875$			1.18848i			0.0401779i
$876$		−	11.1295i		−	0.376032i
$877$	1.09866	−	1.09866i	0.0370990	−	0.0370990i	−0.688314	−	0.725413i	$-0.741649\pi$
$877$	1.09866	−	1.09866i	0.0370990	−	0.0370990i	0.725413	+	0.688314i	$0.241649\pi$
$878$	−0.305631	+	0.305631i	−0.0103145	+	0.0103145i
$879$	1.38712	+	1.38712i	0.0467864	+	0.0467864i
$880$	1.77207			0.0597363
$881$	19.2497	+	19.2497i	0.648540	+	0.648540i	0.952640	−	0.304100i	$-0.0983557\pi$
$881$	19.2497	+	19.2497i	0.648540	+	0.648540i	−0.304100	+	0.952640i	$0.598356\pi$
$882$			11.8329i			0.398434i
$883$	41.7225			1.40407			0.702037	−	0.712140i	$-0.252274\pi$
$883$	41.7225			1.40407			0.702037	+	0.712140i	$0.252274\pi$
$884$	1.25798	+	1.68639i	0.0423104	+	0.0567194i
$885$	2.84685			0.0956959
$886$			1.71673i			0.0576746i
$887$	−5.40672	−	5.40672i	−0.181540	−	0.181540i	0.610487	−	0.792027i	$-0.290974\pi$
$887$	−5.40672	−	5.40672i	−0.181540	−	0.181540i	−0.792027	+	0.610487i	$0.790974\pi$
$888$	−4.59275			−0.154123
$889$	3.77161	+	3.77161i	0.126496	+	0.126496i
$890$	5.06529	−	5.06529i	0.169789	−	0.169789i
$891$	11.5864	−	11.5864i	0.388160	−	0.388160i
$892$			22.9409i			0.768120i
$893$		−	51.6212i		−	1.72744i
$894$	−2.75295	+	2.75295i	−0.0920724	+	0.0920724i
$895$	−17.1912	+	17.1912i	−0.574637	+	0.574637i
$896$	−7.72775	−	7.72775i	−0.258166	−	0.258166i
$897$	0.775063			0.0258786
$898$	1.19652	+	1.19652i	0.0399284	+	0.0399284i
$899$		−	15.3161i		−	0.510822i
$900$	3.74681			0.124894
$901$	−26.4793	+	19.7525i	−0.882155	+	0.658053i
$902$	14.6192			0.486767
$903$		−	4.41953i		−	0.147073i
$904$	30.9190	+	30.9190i	1.02835	+	1.02835i
$905$	−11.8866			−0.395123
$906$	−3.95948	−	3.95948i	−0.131545	−	0.131545i
$907$	30.7988	−	30.7988i	1.02266	−	1.02266i	0.0229217	−	0.999737i	$-0.492703\pi$
$907$	30.7988	−	30.7988i	1.02266	−	1.02266i	0.999737	−	0.0229217i	$-0.00729683\pi$
$908$	−6.97585	+	6.97585i	−0.231502	+	0.231502i
$909$		−	0.800799i		−	0.0265608i
$910$		−	0.342770i		−	0.0113627i
$911$	−23.4200	+	23.4200i	−0.775938	+	0.775938i	−0.979137	−	0.203200i	$-0.934866\pi$
$911$	−23.4200	+	23.4200i	−0.775938	+	0.775938i	0.203200	+	0.979137i	$0.434866\pi$
$912$	1.76759	−	1.76759i	0.0585308	−	0.0585308i
$913$	7.20838	+	7.20838i	0.238562	+	0.238562i
$914$	7.41867			0.245388
$915$	−3.12962	−	3.12962i	−0.103462	−	0.103462i
$916$		−	2.03453i		−	0.0672226i
$917$	11.1039			0.366682
$918$	1.44560	−	9.93532i	0.0477120	−	0.327915i
$919$	22.9512			0.757089			0.378545	−	0.925583i	$-0.376425\pi$
$919$	22.9512			0.757089			0.378545	+	0.925583i	$0.376425\pi$
$920$			10.2496i			0.337919i
$921$	−12.8759	−	12.8759i	−0.424274	−	0.424274i
$922$	13.0563			0.429987
$923$	−3.09443	−	3.09443i	−0.101855	−	0.101855i
$924$	1.62152	−	1.62152i	0.0533440	−	0.0533440i
$925$	−2.24619	+	2.24619i	−0.0738543	+	0.0738543i
$926$			11.2616i			0.370078i
$927$		−	46.0516i		−	1.51253i
$928$	9.56200	−	9.56200i	0.313888	−	0.313888i
$929$	−13.6260	+	13.6260i	−0.447055	+	0.447055i	−0.894374	−	0.447320i	$-0.852379\pi$
$929$	−13.6260	+	13.6260i	−0.447055	+	0.447055i	0.447320	+	0.894374i	$0.352379\pi$
$930$	2.00030	+	2.00030i	0.0655923	+	0.0655923i
$931$	36.9412			1.21070
$932$	22.7068	+	22.7068i	0.743787	+	0.743787i
$933$			7.51853i			0.246146i
$934$	−10.1169			−0.331036
$935$	−6.29687	−	8.44129i	−0.205930	−	0.276060i
$936$	−2.63977			−0.0862836
$937$		−	23.6659i		−	0.773132i	−0.922262	−	0.386566i	$-0.873661\pi$
$937$		−	23.6659i		−	0.773132i	0.922262	−	0.386566i	$-0.126339\pi$
$938$	5.23155	+	5.23155i	0.170816	+	0.170816i
$939$	16.6601			0.543681
$940$	−7.65307	−	7.65307i	−0.249616	−	0.249616i
$941$	2.22184	−	2.22184i	0.0724298	−	0.0724298i	−0.669964	−	0.742394i	$-0.733690\pi$
$941$	2.22184	−	2.22184i	0.0724298	−	0.0724298i	0.742394	+	0.669964i	$0.233690\pi$
$942$	6.05332	−	6.05332i	0.197228	−	0.197228i
$943$		−	28.2240i		−	0.919100i
$944$			3.62421i			0.117958i
$945$	2.61190	−	2.61190i	0.0849652	−	0.0849652i
$946$	9.65541	−	9.65541i	0.313924	−	0.313924i
$947$	27.0812	+	27.0812i	0.880020	+	0.880020i	0.993536	−	0.113516i	$-0.0362114\pi$
$947$	27.0812	+	27.0812i	0.880020	+	0.880020i	−0.113516	+	0.993536i	$0.536211\pi$
$948$	0.614305			0.0199517
$949$	3.83491	+	3.83491i	0.124486	+	0.124486i
$950$			5.17986i			0.168057i
$951$	−1.75319			−0.0568511
$952$	−1.87183	+	12.8647i	−0.0606664	+	0.416947i
$953$	−34.0185			−1.10197			−0.550984	−	0.834516i	$-0.685747\pi$
$953$	−34.0185			−1.10197			−0.550984	+	0.834516i	$0.685747\pi$
$954$		−	16.9677i		−	0.549349i
$955$	12.2280	+	12.2280i	0.395688	+	0.395688i
$956$	−8.91654			−0.288381
$957$	2.27541	+	2.27541i	0.0735535	+	0.0735535i
$958$	−3.33062	+	3.33062i	−0.107607	+	0.107607i
$959$	−7.12493	+	7.12493i	−0.230076	+	0.230076i
$960$			1.74141i			0.0562037i
$961$			12.8947i			0.415958i
$962$	0.647826	−	0.647826i	0.0208868	−	0.0208868i
$963$	−7.27969	+	7.27969i	−0.234585	+	0.234585i
$964$	26.8526	+	26.8526i	0.864864	+	0.864864i
$965$	−1.80952			−0.0582505
$966$	1.38628	+	1.38628i	0.0446029	+	0.0446029i
$967$		−	33.0762i		−	1.06366i	−0.846852	−	0.531829i	$-0.821505\pi$
$967$		−	33.0762i		−	1.06366i	0.846852	−	0.531829i	$-0.178495\pi$
$968$	−11.8750			−0.381678
$969$	−14.7009	−	2.13901i	−0.472263	−	0.0687148i
$970$	−5.53479			−0.177711
$971$		−	22.1601i		−	0.711152i	−0.934647	−	0.355576i	$-0.884285\pi$
$971$		−	22.1601i		−	0.711152i	0.934647	−	0.355576i	$-0.115715\pi$
$972$	−12.5659	−	12.5659i	−0.403051	−	0.403051i
$973$	7.13921			0.228873
$974$	18.3380	+	18.3380i	0.587587	+	0.587587i
$975$	0.141856	−	0.141856i	0.00454304	−	0.00454304i
$976$	3.98419	−	3.98419i	0.127531	−	0.127531i
$977$		−	15.7856i		−	0.505025i	−0.967594	−	0.252513i	$-0.918743\pi$
$977$		−	15.7856i		−	0.505025i	0.967594	−	0.252513i	$-0.0812570\pi$
$978$		−	6.09329i		−	0.194842i
$979$	−16.5132	+	16.5132i	−0.527765	+	0.527765i
$980$	5.47671	−	5.47671i	0.174947	−	0.174947i
$981$	23.0072	+	23.0072i	0.734562	+	0.734562i
$982$	14.7062			0.469293
$983$	−27.4094	−	27.4094i	−0.874223	−	0.874223i	0.118706	−	0.992929i	$-0.462125\pi$
$983$	−27.4094	−	27.4094i	−0.874223	−	0.874223i	−0.992929	+	0.118706i	$0.962125\pi$
$984$		−	10.5623i		−	0.336713i
$985$	−16.5784			−0.528231
$986$	−7.39000	−	1.07525i	−0.235345	−	0.0342431i
$987$	−5.05713			−0.160970
$988$			3.37360i			0.107329i
$989$	−18.6408	−	18.6408i	−0.592744	−	0.592744i
$990$	5.40909			0.171912
$991$	−22.6272	−	22.6272i	−0.718776	−	0.718776i	0.249578	−	0.968355i	$-0.419708\pi$
$991$	−22.6272	−	22.6272i	−0.718776	−	0.718776i	−0.968355	+	0.249578i	$0.919708\pi$
$992$	−27.4038	+	27.4038i	−0.870073	+	0.870073i
$993$	11.4696	−	11.4696i	0.363978	−	0.363978i
$994$		−	11.0694i		−	0.351102i
$995$			25.1610i			0.797657i
$996$	2.13195	−	2.13195i	0.0675535	−	0.0675535i
$997$	−9.85607	+	9.85607i	−0.312145	+	0.312145i	−0.845740	−	0.533595i	$-0.820841\pi$
$997$	−9.85607	+	9.85607i	−0.312145	+	0.312145i	0.533595	+	0.845740i	$0.320841\pi$
$998$	−3.95800	−	3.95800i	−0.125288	−	0.125288i
$999$	9.87286			0.312363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.e.a.81.5	yes	12
3.2	odd	2		765.2.k.b.676.2		12
4.3	odd	2		1360.2.bt.d.81.2		12
5.2	odd	4		425.2.j.c.149.2		12
5.3	odd	4		425.2.j.b.149.5		12
5.4	even	2		425.2.e.f.251.2		12
17.2	even	8		1445.2.a.o.1.2		6
17.4	even	4	inner	85.2.e.a.21.2	✓	12
17.8	even	8		1445.2.d.g.866.9		12
17.9	even	8		1445.2.d.g.866.10		12
17.15	even	8		1445.2.a.n.1.2		6
51.38	odd	4		765.2.k.b.361.5		12
68.55	odd	4		1360.2.bt.d.1041.2		12
85.4	even	4		425.2.e.f.276.5		12
85.19	even	8		7225.2.a.z.1.5		6
85.38	odd	4		425.2.j.c.174.2		12
85.49	even	8		7225.2.a.bb.1.5		6
85.72	odd	4		425.2.j.b.174.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.2	✓	12	17.4	even	4	inner
85.2.e.a.81.5	yes	12	1.1	even	1	trivial
425.2.e.f.251.2		12	5.4	even	2
425.2.e.f.276.5		12	85.4	even	4
425.2.j.b.149.5		12	5.3	odd	4
425.2.j.b.174.5		12	85.72	odd	4
425.2.j.c.149.2		12	5.2	odd	4
425.2.j.c.174.2		12	85.38	odd	4
765.2.k.b.361.5		12	51.38	odd	4
765.2.k.b.676.2		12	3.2	odd	2
1360.2.bt.d.81.2		12	4.3	odd	2
1360.2.bt.d.1041.2		12	68.55	odd	4
1445.2.a.n.1.2		6	17.15	even	8
1445.2.a.o.1.2		6	17.2	even	8
1445.2.d.g.866.9		12	17.8	even	8
1445.2.d.g.866.10		12	17.9	even	8
7225.2.a.z.1.5		6	85.19	even	8
7225.2.a.bb.1.5		6	85.49	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.783476i q^{2} +(0.385357 + 0.385357i) q^{3} +1.38617 q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.301918 + 0.301918i) q^{6} +(-0.840380 + 0.840380i) q^{7} +2.65298i q^{8} -2.70300i q^{9} +(0.554001 - 0.554001i) q^{10} +(-1.80608 + 1.80608i) q^{11} +(0.534168 + 0.534168i) q^{12} -0.368117 q^{13} +(-0.658417 - 0.658417i) q^{14} -0.544977i q^{15} +0.693788 q^{16} +(-2.46531 - 3.30488i) q^{17} +2.11773 q^{18} -6.61138i q^{19} +(-0.980167 - 0.980167i) q^{20} -0.647692 q^{21} +(-1.41502 - 1.41502i) q^{22} +(-2.73186 + 2.73186i) q^{23} +(-1.02234 + 1.02234i) q^{24} +1.00000i q^{25} -0.288411i q^{26} +(2.19769 - 2.19769i) q^{27} +(-1.16491 + 1.16491i) q^{28} +(-1.63466 - 1.63466i) q^{29} +0.426976 q^{30} +(4.68480 + 4.68480i) q^{31} +5.84952i q^{32} -1.39197 q^{33} +(2.58929 - 1.93151i) q^{34} +1.18848 q^{35} -3.74681i q^{36} +(2.24619 + 2.24619i) q^{37} +5.17986 q^{38} +(-0.141856 - 0.141856i) q^{39} +(1.87594 - 1.87594i) q^{40} +(-5.16572 + 5.16572i) q^{41} -0.507451i q^{42} +6.82350i q^{43} +(-2.50353 + 2.50353i) q^{44} +(-1.91131 + 1.91131i) q^{45} +(-2.14034 - 2.14034i) q^{46} +7.80793 q^{47} +(0.267356 + 0.267356i) q^{48} +5.58752i q^{49} -0.783476 q^{50} +(0.323534 - 2.22358i) q^{51} -0.510272 q^{52} -8.01219i q^{53} +(1.72184 + 1.72184i) q^{54} +2.55419 q^{55} +(-2.22951 - 2.22951i) q^{56} +(2.54774 - 2.54774i) q^{57} +(1.28072 - 1.28072i) q^{58} +5.22381i q^{59} -0.755428i q^{60} +(5.74267 - 5.74267i) q^{61} +(-3.67043 + 3.67043i) q^{62} +(2.27155 + 2.27155i) q^{63} -3.19538 q^{64} +(0.260298 + 0.260298i) q^{65} -1.09058i q^{66} -7.94564 q^{67} +(-3.41733 - 4.58111i) q^{68} -2.10548 q^{69} +0.931143i q^{70} +(8.40610 + 8.40610i) q^{71} +7.17100 q^{72} +(-10.4176 - 10.4176i) q^{73} +(-1.75984 + 1.75984i) q^{74} +(-0.385357 + 0.385357i) q^{75} -9.16447i q^{76} -3.03559i q^{77} +(0.111141 - 0.111141i) q^{78} +(0.575011 - 0.575011i) q^{79} +(-0.490582 - 0.490582i) q^{80} -6.41521 q^{81} +(-4.04721 - 4.04721i) q^{82} -3.99116i q^{83} -0.897809 q^{84} +(-0.593666 + 4.08014i) q^{85} -5.34604 q^{86} -1.25986i q^{87} +(-4.79150 - 4.79150i) q^{88} +9.14311 q^{89} +(-1.49746 - 1.49746i) q^{90} +(0.309359 - 0.309359i) q^{91} +(-3.78681 + 3.78681i) q^{92} +3.61064i q^{93} +6.11732i q^{94} +(-4.67495 + 4.67495i) q^{95} +(-2.25415 + 2.25415i) q^{96} +(-4.99529 - 4.99529i) q^{97} -4.37769 q^{98} +(4.88185 + 4.88185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Introduction

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